Accelerated Convergence in Newton's Method

Newton’s Method is based on a linear approximation of the function whose roots are to be determined taken at the current point, and the resulting algorithm is known to converge quadratically. In a procedure to increase the rate of convergence the author modifies the target function in such a way that Newton’s Method applied to the modified function will yield a faster rate of convergence.

[1]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.